The current in a charging capacitor is given by Eq. (26.13).
(a) The instantaneous power supplied by the battery is Ei. Integrate this to find the total energy supplied by the battery.
(b) The instantaneous power dissipated in the resistor is i2R. Integrate this to find the total energy dissipated in the resistor.
(c) Find the final energy stored in the capacitor, and show that this equals the total energy supplied by the battery less the energy dissipated in the resistor, as obtained in parts (a) and (b).
(d) What fraction of the energy supplied by the battery is stored in the capacitor? How does this fraction depend on R?